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Connectivity-Preserving Multi-Agent Area Coverage via Optimal-Transport-Based Density-Driven Optimal Control (D2OC)

Kooktae Lee, Ethan Brook

TL;DR

The paper tackles non-uniform area coverage by multi-agent systems while maintaining inter-agent connectivity. It extends the Density-Driven Optimal Control (D$^2$OC) framework by integrating a Wasserstein-distance–based coverage objective with a connectivity-preserving soft penalty, formulated as a convex quadratic program and solvable in a distributed fashion. Key contributions include (i) establishing QP equivalence and convexity of the unconstrained D$^2$OC cost, (ii) introducing a reachable-set based, smooth connectivity penalty that preserves communication without rigid formations, and (iii) demonstrating via simulations that the approach improves convergence speed and coverage quality while maintaining connectivity. This connectivity-aware, scalable method enhances practical deployment of multi-robot networks for non-uniform area coverage across applications such as search-and-rescue and environmental monitoring.

Abstract

Multi-agent systems play a central role in area coverage tasks across search-and-rescue, environmental monitoring, and precision agriculture. Achieving non-uniform coverage, where spatial priorities vary across the domain, requires coordinating agents while respecting dynamic and communication constraints. Density-driven approaches can distribute agents according to a prescribed reference density, but existing methods do not ensure connectivity. This limitation often leads to communication loss, reduced coordination, and degraded coverage performance. This letter introduces a connectivity-preserving extension of the Density-Driven Optimal Control (D2OC) framework. The coverage objective, defined using the Wasserstein distance between the agent distribution and the reference density, admits a convex quadratic program formulation. Communication constraints are incorporated through a smooth connectivity penalty, which maintains strict convexity, supports distributed implementation, and preserves inter-agent communication without imposing rigid formations. Simulation studies show that the proposed method consistently maintains connectivity, improves convergence speed, and enhances non-uniform coverage quality compared with density-driven schemes that do not incorporate explicit connectivity considerations.

Connectivity-Preserving Multi-Agent Area Coverage via Optimal-Transport-Based Density-Driven Optimal Control (D2OC)

TL;DR

The paper tackles non-uniform area coverage by multi-agent systems while maintaining inter-agent connectivity. It extends the Density-Driven Optimal Control (DOC) framework by integrating a Wasserstein-distance–based coverage objective with a connectivity-preserving soft penalty, formulated as a convex quadratic program and solvable in a distributed fashion. Key contributions include (i) establishing QP equivalence and convexity of the unconstrained DOC cost, (ii) introducing a reachable-set based, smooth connectivity penalty that preserves communication without rigid formations, and (iii) demonstrating via simulations that the approach improves convergence speed and coverage quality while maintaining connectivity. This connectivity-aware, scalable method enhances practical deployment of multi-robot networks for non-uniform area coverage across applications such as search-and-rescue and environmental monitoring.

Abstract

Multi-agent systems play a central role in area coverage tasks across search-and-rescue, environmental monitoring, and precision agriculture. Achieving non-uniform coverage, where spatial priorities vary across the domain, requires coordinating agents while respecting dynamic and communication constraints. Density-driven approaches can distribute agents according to a prescribed reference density, but existing methods do not ensure connectivity. This limitation often leads to communication loss, reduced coordination, and degraded coverage performance. This letter introduces a connectivity-preserving extension of the Density-Driven Optimal Control (D2OC) framework. The coverage objective, defined using the Wasserstein distance between the agent distribution and the reference density, admits a convex quadratic program formulation. Communication constraints are incorporated through a smooth connectivity penalty, which maintains strict convexity, supports distributed implementation, and preserves inter-agent communication without imposing rigid formations. Simulation studies show that the proposed method consistently maintains connectivity, improves convergence speed, and enhances non-uniform coverage quality compared with density-driven schemes that do not incorporate explicit connectivity considerations.

Paper Structure

This paper contains 17 sections, 3 theorems, 28 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Wasserstein Distance and Optimal Transport
  4. Decentralized Coverage Protocol
  5. Formulation of the D$^2$OC Cost Function via Quadratic Programming
  6. Connectivity-Preserving D$^2$OC
  7. Connectivity Constraint with Reachable Sets
  8. Soft-Constraint for Connectivity-Preserving Control
  9. Convexity of the distance term
  10. Convexity and monotonicity of the scalar penalty
  11. Composition with shifted distance
  12. Sum of convex terms and box constraints
  13. Existence of minimizers
  14. Uniqueness under $H_i \succ 0$
  15. KKT characterization
  16. ...and 2 more sections

Key Result

Proposition 1

Let $\mathcal{S}_i(k+h)$ denote the index set of local sample points for agent $i$ at time $k+h$. Let the transport weights $\pi_j(k+h) \ge 0$ be locally computed over the prediction window $h = r,\ldots,r+H{-}1$ based on the selected local samples. Define the weighted barycenter at $k+h$ as $\bar{q With 'const.' denoting all terms independent of $Y_i^{k|r:H}$, we have

Figures (1)

  • Figure 1: Twenty-agent D$^2$OC simulation: trajectories (left) and inter-agent distances (right) without/with connectivity constraints. Red dashed: communication threshold; black dashed: minimum distance.

Theorems & Definitions (11)

  • Definition 1: Output Relative Degree of a Discrete-Time LTI System
  • Proposition 1
  • proof
  • Theorem 1: Uniqueness of the Unconstrained Optimal Input
  • proof
  • Remark 1: Extension to Collision Avoidance
  • Remark 2: Robustness to Communication Delays and Uncertainties
  • Theorem 2: Strict Convexity of Soft-Constraint Control with Box Constraints
  • proof
  • Remark 3: Soft Connectivity and Effect of Penalty Parameters
  • ...and 1 more